Problem: Li Na is going to plant $63$ tomato plants and $81$ rhubarb plants. Li Na would like to plant the plants in rows where each row has the same number of tomato plants and each row has the same number of rhubarb plants. What is the greatest number of rows Li Na can plant?
Solution: In order to know how many rows Li Na can plant, we need a number that is a factor of ${63}$ and ${81}$, so that the ${63}$ tomato plants and the ${81}$ rhubarb plants can be divided up evenly. So, if there were $\gray{3}$ rows, there would be ${63} \div \gray{3} =21$ tomato plants and ${81} \div \gray{3} =27$ rhubarb plants in each row. This creates rows with the same number of tomato plants and rhubarb plants, but it isn't the greatest number of rows! To find the greatest number of rows of plants, we want to find the greatest common factor of ${63}$ and ${81}$. To do so, let's find factors of ${63}$ and ${81}$. ${63}$ : $1,3, 7, 9, 21, 63$ ${81}$ : $1, 3, 9, 27, 81$ The greatest common factor of ${63}$ and ${81}$ is $9$. In math notation this looks like: $ \text{gcf}({63},{81}) = 9$. The greatest number of rows that Li Na can plant is $9$.